Question

Obtain an expression for torque acting on a rotating body with constant angular acceleration. Hence state the dimensions and SI unit of torque.

Answer 1

A system rotating with an angular momentum in presence of a torque suffers a change in the angular momentum and the rate of change of angular momentum is directly proportional to the torque acting on it.
If I be the moment of inertia of the system and $\omega$ be the angular velocity then angular momentum $L=I\omega$
Rate of change of angular momentum provided the shape of system does not change is :
$\tau =\frac{d}{dt}\left(I\omega \right)=I\frac{d\omega }{dt}=I\alpha$
$\alpha$ is the angular acceleration and $\tau$ is the torque.
Dimension of Torque is $\left[M{L}^2{T}^{-2}\right]$ and its unit is Newton- metre (N⋅m).